Abstract-A heterogenous network with base stations (BSs), small base stations (SBSs) and users distributed according to independent Poisson point processes is considered. SBS nodes are assumed to possess high storage capacity and to form a distributed caching network. Popular files are stored in local caches of SBSs, so that a user can download the desired files from one of the SBSs in its vicinity. The offloading-loss is captured via a cost function that depends on the random caching strategy proposed here. The popularity profile of cached content is unknown and estimated using instantaneous demands from users within a specified time interval. An estimate of the cost function is obtained from which an optimal random caching strategy is devised. The training time to achieve an ǫ > 0 difference between the achieved and optimal costs is finite provided the user density is greater than a predefined threshold, and scales as N 2 , where N is the support of the popularity profile. A transfer learningbased approach to improve this estimate is proposed. The training time is reduced when the popularity profile is modeled using a parametric family of distributions; the delay is independent of N and scales linearly with the dimension of the distribution parameter.

Caching popular contents in advance is an important technique to achieve low latency and reduce the backhaul costs in future wireless communications. Considering a network with base stations distributed as a Poisson point process, optimal content placement caching probabilities are obtained to maximize the average success probability (ASP) for a known content popularity (CP) profile, which in practice is time-varying and unknown in advance. In this paper, we first propose two online prediction (OP) methods for forecasting CP viz., popularity prediction model (PPM) and Grassmannian prediction model (GPM), where the unconstrained coefficients for linear prediction are obtained by solving constrained non-negative least squares. To reduce the higher computational complexity per online round, two online learning (OL) approaches viz., weighted-follow-theleader and weighted-follow-the-regularized-leader are proposed, inspired by the OP models. In OP, ASP difference (i.e, the gap between the ASP achieved by prediction and that by known content popularity) is bounded, while in OL, sub-linear MSE regret and linear ASP regret bounds are obtained. With MovieLens dataset, simulations verify that OP methods are better for MSE and ASP difference minimization, while the OL approaches perform well for the minimization of the MSE and ASP regrets.

Content caching at the small-cell base stations (sBSs) in a heterogeneous wireless network is considered. A cost function is proposed that captures the backhaul link load called the "offloading loss", which measures the fraction of the requested files that are not available in the sBS caches.As opposed to the previous approaches that consider time-invariant and perfectly known popularity profile, caching with non-stationary and statistically dependent popularity profiles (assumed unknown, and hence, estimated) is studied from a learning-theoretic perspective. A probably approximately correct result is derived, which presents a high probability bound on the offloading loss difference, i.e., the error between the estimated and the optimal offloading loss. The difference is a function of the Rademacher complexity, the β−mixing coefficient, the number of time slots, and a measure of discrepancy between the estimated and true popularity profiles. A cache update algorithm is proposed, and simulation results are presented to show its superiority over periodic updates. The performance analyses for Bernoulli and Poisson request models are also presented. Index TermsCaching; time-varying popularity profiles; probably approximately correct (PAC) learning.

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Abstract-A heterogenous network is considered where the base stations (BSs), small base stations (SBSs) and users are distributed according to independent Poisson point processes (PPPs). We let the SBS nodes to posses high storage capacity and are assumed to form a distributed caching network. Popular data files are stored in the local cache of SBS, so that users can download the desired files from one of the SBS in the vicinity subject to availability. The offloading-loss is captured via a cost function that depends on a random caching strategy proposed in this paper. The cost function depends on the popularity profile, which is, in general, unknown. In this work, the popularity profile is estimated at the BS using the available instantaneous demands from the users in a time interval [0, τ ]. This is then used to find an estimate of the cost function from which the optimal random caching strategy is devised. The main results of this work are the following: First it is shown that the waiting time τ to achieve an ǫ > 0 difference between the achieved and optimal costs is finite, provided the user density is greater than a predefined threshold. In this case, τ is shown to scale as N 2 , where N is the support of the popularity profile. Secondly, a transfer learning-based approach is proposed to obtain an estimate of the popularity profile used to compute the empirical cost function. A condition is derived under which the proposed transfer learning-based approach performs better than the random caching strategy.

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